3rd Edition
Classical Feedback Control with Nonlinear Multi-Loop Systems With MATLAB® and Simulink®, Third Edition
Classical Feedback Control with Nonlinear Multi-Loop Systems describes the design of high-performance feedback control systems, emphasizing the frequency-domain approach widely used in practical engineering. It presents design methods for high-order nonlinear single- and multi-loop controllers with efficient analog and digital implementations. Bode integrals are employed to estimate the available system performance and to determine the ideal frequency responses that maximize the disturbance rejection and feedback bandwidth. Nonlinear dynamic compensators provide global stability and improve transient responses. This book serves as a unique text for an advanced course in control system engineering, and as a valuable reference for practicing engineers competing in today’s industrial environment.
Preface
To Instructors
- Feedback and Sensitivity
- Feedforward, Multi-loop, and MIMO Systems
- Frequency Response Methods
- Shaping the Loop Frequency Response
- Compensator Design
- Analog Controller Implementation
- Linear Links and System Simulation
- Introduction to Alternative Methods of Controller Design
- Adaptive Systems
- Provision of Global Stability
- Describing Functions
- Process Instability
- Multiwindow Controllers
- Nonlinear Multi-Loop Systems with Uncertainty
1.1 Feedback Control System
1.2 Feedback: Positive and Negative
1.3 Large Feedback
1.4 Loop Gain and Phase Frequency Responses
1.5 Disturbance Rejection
1.6 Example of System Analysis
1.7 Effect of Feedback on the Actuator Nondynamic Nonlinearity
1.8 Sensitivity
1.9 Effect of Finite Plant Parameter Variations
1.10 Automatic Signal Level Control
1.11 Lead and PID Compensators
1.12 Conclusion and a Look Ahead
Problems
Answers to Selected Problems
2.1 Command Feedforward
2.2 Prefilter and the Feedback Path Equivalent
2.3 Error Feedforward
2.4 Black’s Feedforward
2.5 Multi-loop Feedback Systems
2.6 Local, Common, and Nested Loops
2.7 Crossed Loops and Main/Vernier Loops
2.8 Block Diagram Manipulations and Transfer Function Calculations
2.9 MIMO Feedback Systems
Problems
3.1 Conversion of Time Domain Requirements to Frequency Domain
3.2 Closed-Loop Transient Response
3.3 Root Locus
3.4 Nyquist Stability Criterion
3.5 Robustness and Stability Margins
3.6 Nyquist Criterion for Unstable Plants
3.7 Successive Loop Closure Stability Criterion (Bode-Nyquist)
3.8 Nyquist Diagrams for Loop Transfer Functions with Poles at the Origin
3.9 Bode Phase-Gain Relation
3.10 Phase Calculations
3.11 From the Nyquist Diagram to the Bode Diagram
3.12 Non-minimum Phase Lag
3.13 Ladder Networks and Parallel Connections of M.P. Links
3.14 Other Bode Definite Integrals
Problems
Answers to Selected Problems
4.1 Optimality of the Compensator Design
4.2 Feedback Maximization
4.3 Feedback Bandwidth Limitations
4.4 Coupling in MIMO Systems
4.5 Shaping Parallel Channel Responses
Problems
Answers to Selected Problems
5.1 Loop Shaping Accuracy
5.2 Asymptotic Bode Diagram
5.3 Approximation of Constant Slope Gain Response
5.4 Lead and Lag Links
5.5 Complex Poles
5.6 Cascaded Links
5.7 Parallel Connection of Links
5.8 Simulation of a PID Controller
5.9 Analog and Digital Controllers
5.10 Digital Compensator Design
Problems
Answers to Selected Problems
6.1 Active RC Circuits
6.2 Design and Iterations in the Element Value Domain
6.3 Analog Compensator, Analog or Digitally Controlled
6.4 Switched-Capacitor Filters
6.5 Miscellaneous Hardware Issues
6.6 PID Tunable Controller
6.7 Tunable Compensator with One Variable Parameter
6.8 Loop Response Measurements
Problems
Answers to Selected Problems
7.1 Mathematical Analogies
7.2 Junctions of Unilateral Links
7.3 Effect of the Plant and Actuator Impedances on the Plant Transfer Function Uncertainty
7.4 Effect of Feedback on the Impedance (Mobility)
7.5 Effect of Load Impedance on Feedback
7.6 Flowchart for Chain Connection of Bidirectional Two-Ports
7.7 Examples of System Modeling
7.8 Flexible Structures
7.9 Sensor Noise
7.10 Mathematical Analogies to the Feedback System
7.11 Linear Time-Variable Systems
Problems
Answers to Selected Problems
8.1 QFT
8.2 Root Locus and Pole Placement Methods
8.3 State-Space Methods and Full-State Feedback
8.4 LQR and LQG
8.5 H8, µ-Synthesis, and Linear Matrix Inequalities
9.1 Benefits of Adaptation to the Plant Parameter Variations
9.2 Static and Dynamic Adaptation
9.3 Plant Transfer Function Identification
9.4 Flexible and N. P. Plants
9.5 Disturbance and Noise Rejection
9.6 Pilot Signals and Dithering Systems
9.7 Adaptive Filters
10.1 Nonlinearities of the Actuator, Feedback Path, and Plant
10.2 Types of Self-Oscillation
10.3 Stability Analysis of Nonlinear Systems
10.4 Absolute Stability
10.5 Popov Criterion
10.6 Applications of Popov Criterion
10.7 Absolutely Stable Systems with Nonlinear Dynamic Compensation
Problems
Answers to Selected Problems
11.1 Harmonic Balance
11.2 Describing Function
11.3 Describing Functions for Symmetrical Piece-Linear Characteristics
11.4 Hysteresis
11.5 Nonlinear Links Yielding Phase Advance for Large-Amplitude Signals
11.6 Two Nonlinear Links in the Feedback Loop
11.7 NDC with a Single Nonlinear Nondynamic Link
11.8 NDC with Parallel Channels
11.9 NDC Made with Local Feedback
11.10 Negative Hysteresis and Clegg Integrator
11.11 Nonlinear Interaction between the Local and the Common Feedback Loops
11.12 NDC in Multi-loop Systems
11.13 Harmonics and Intermodulation
11.14 Verification of Global Stability
Problems
Answers to Selected Problems
12.1 Process Instability
12.2 Absolute Stability of the Output Process
12.3 Jump Resonance
12.4 Subharmonics
12.5 Nonlinear Dynamic Compensation
Problems
13.1 Composite Nonlinear Controllers
13.2 Multiwindow Control
13.3 Switching from a Hot Controller to a Cold Controller
13.4 Wind-Up and Anti-Wind-Up Controllers
13.5 Selection Order
13.6 Acquisition and Tracking
13.7 Time-Optimal Control
13.8 Examples
Problems
14.1 Systems with High-Frequency Plant Uncertainty
14.2 Stability and Multi-frequency Oscillations in Band-Pass Systems
14.3 Bode Single-loop Systems
14.4 Multi-Input Multi-Output Systems
14.5 Nonlinear Multi-loop Feedback
14.6 Design of the Internal Loops
14.7 Input Signal Reconstruction
Appendix 1: Feedback Control, Elementary Treatment
Appendix 2: Frequency Responses
Appendix 3: Causal Systems, Passive Systems, Positive Real Functions, and Collocated Control
Appendix 4: Derivation of Bode Integrals
Appendix 5: Program for Phase Calculation
Appendix 6: Generic Single-Loop Feedback System
Appendix 7: Effect of Feedback on Mobility
Appendix 8: Regulation
Appendix 9: Balanced Bridge Feedback
Appendix 10: Phase-Gain Relation for Describing Functions
Appendix 11: Discussions
Appendix 12: Design Sequence
Appendix 13: Examples
Appendix 14: Bode Step Toolbox
Appendix 15: Nonlinear Multi-loop Feedback Control (Patent Application)
Bibliography
Notation
Index
Biography
Boris J. Lurie worked for many years in the telecommunication and aerospace industries, and taught at Russian, Israeli, and American universities. He was a senior staff member of the Jet Propulsion Laboratory, California Institute of Technology.
Paul J. Enright currently works in the field of quantitative finance in Chicago. As a member of the technical staff at the Jet Propulsion Laboratory, California Institute of Technology, he designed attitude control systems for interplanetary spacecraft and conducted research in nonlinear control.
